Hi,
You need the two buttons, because the system needs that the address is registered to continue the checkout.
When clicking on submit, the page is reloaded with the addresses listing displayed. And then you have to click on "Next".
I suggest to change the actual "Submit" to "Save" or something like that.
Else a way could be to set a parameter in post when clicking on "Submit", then add some javascript to submit the form again if the post var is present.
It will reload the page twice and go to the next step. It require some JavaScript and PHP knowledge.